Xbond wrote:Hi there,
I completely lost with this PS. Could you help me to undersatand the concept in simple way;
To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid ?
a) x/T
b) x/(T-S)
c) Sx/(T-S)
d) Sx/ T(T-S)
e) x(T-S)/t
When we have complicated word problems, making sense of them is important; the GMAT isn't just about understanding the math, understanding the real life situation can make our lives a lot easier.
Here, we have a bunch of coworkers who were going to chip in for a retirement party. However, a number of them turned out to be deadbeats and didn't chip in. The question: how much extra do the other workers have to pay to make up for the deadbeats?
We could solve this algebraically, but it's a great question for picking numbers: a complicated word problem and complicated variable expressions in the answer choices. Rather than doing the math, let's pick some real numbers and see what result we get.
Our variables:
T: original number of contributors
S: number of workers who said they'd pay, but didn't
x: total cost of the party
We want to pick numbers that will work out fairly nicely, so let's try:
x = $120
T = 15 (goes into 120)
S = 5 (which leaves us with 10 people who do pay, which also goes into 120).
Now let's answer the question:
Originally we had $120 spread out among 15 workers... 120/15 = $8 each.
Now we have $120 spread out among 10 workers.. 120/10 = $12 each.
How much extra do the non-deadbeats have to pay? $12 - $8 = $4 each.
Next up, check the choices:
a) x/T = 120/15 = 8... wrong!
b) x/(T-S) = 120/(15-5) = 120/10 = 12... wrong!
c) Sx/(T-S) = 5*120/(15-5) = 600/10 = 60... wrong!
d) Sx/ T(T-S) = 5*120/15(15-5) = 600/(15*10) = 600/150 = 4... ding ding!
e) x(T-S)/t = 120(15-5)/15 = 120(10)/15 = 1200/15 = a lot more than 4... wrong.
Only (d) worked out, therefore (d) is the correct choice.
Note that we didn't actually have to solve the wrong choices all the way through - as soon as you could see that the results was NOT going to be 4, you could eliminate it and move on.
Of course we also could have solved algebraically, if you were feeling algebraic at the time.
Amount owing = cost/(# of contributors)
Original amount owing per person = x/T
New amount owing per person = x/(T-S)
Difference in the two gives us the additional amount owed per person:
x/(T-S) - x/T
getting a common denominator of T(T-S):
(x(T) - x(T-S)/T(T-S)
x(T+S-T)/T(T-S)
x(S)/T(T-S)... choose (D).
Now the big question: how do I decide when I should pick numbers and when I should do the math?
If the algebra jumps out at you, then setting up the equations will usually be quicker; however, if you don't immediately intuit how to set up the equations, then you need to find another approach to the question, such as picking numbers. The one thing you absolutely CANNOT afford to do during the GMAT is stare at the screen praying for inspiration to strike.
